Practice Questions

Q15.Two point charges q1(√10 μC) and respectively. The electric field (in V/m) at a point y = 3 m on y-axis is, [Take 4πϵ01 = 9 × 109 N m2C−2] + 81 −81 × 102 (1) (−81 ˆi ˆj) × 102 (2) (81 ˆi ˆj) + 27 × 102 (3) (−63 ˆi ˆj) × 102 (4) (63ˆi −27ˆj)

Q15.An electric dipole is formed by two equal and opposite charges q with separation d . The charges have same mass m. It is kept in a uniform electric field E . If it is slightly rotated from its equilibrium orientation, then its angular frequency 𝜔 is: (1) qE (2) 2qE 2√ md √ md (3) qE (4) qE √ 2md √ md

Q15.Three charges Q, +y and +q are placed at the vertices of a right-angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of Q is (1) +q (2) −√2q √2+1 (3) −q (4) −2q 1+√2

Q15.The figure shows a capacitor of capacitance C connected to a battery via a switch, having a total charge Q on it, in steady-state. When the switch S is turned from position A to position B , the energy dissipated in the circuit is (1) 1 Q2 (2) 3 Q2 8 C 8 C (3) 3 Q2 (4) 5 Q2 4 C 8 C JEE Main 2019 (12 Jan Shift 1) JEE Main Previous Year Paper

Q15.A solid conducting sphere, having a charge Q, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V . If the shell is now given a charge of – 4Q, the new potential difference between the same two surfaces is: (1) – 2V (2) 2 V (3) V (4) 4 V

Q15.A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a, would be: (1) Q (2) Q (a2+b2+c2) 4πϵ0(a+b+c) 4πϵ0(a3+b3+c3) (3) Q ab+bc+ca (4) Q(a+b+c) 12πϵ0 abc 4πϵ0(a2+b2+c2)

Q15.A current of 5 A passes through a copper conductor (resistivity = 1.7 × 10−8 Ω m ) of radius of cross-section 5 mm . Find the mobility of the charges if their drift velocity is 1.1 × 10−3 ms−1 . (1) 1.5 m2 V−1 s−1 (2) 1.8 m2 V−1 s−1 (3) 1.0 m2 V−1 s−1 (4) 1.3 m2 V−1 s−1

Q15.A Point dipole →p = - p0^𝑥 at a distance d are, respectively: (Taken V = 0 at infinity) | (1) |→p | -→p (2) |→p 4πε0d2, 4πε0d3 0, 4πε0d3 -→p (3) |→p | →p (4) 4πε0d3 4πε0d3, 4πε0d3 0,

Q15.For a uniformly charged ring of radius 𝑅, the electric field on its axis has the largest magnitude at a distance ℎ from its centre. Then value of ℎ is: (1) 𝑅 (2) 𝑅 √2 √5 (3) 𝑅√2 (4) 𝑅

Q15.When heat Q is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by ∆T . The heat required to produce the same change in temperature, at a constant pressure is: (1) 3 (2) 7 2Q 5Q 5 2 (3) 3Q (4) 3Q

Q16.Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by ρ(r) = kr, where r is the distance from the centre. Two charges A and B , of −Q each, are placed on diametrically opposite points, at equal distance, a, from the centre. If A and B do not experience any force, then: (1) a = 3R1 (2) a = R 2 4 √3 (3) a = 2 −14 R (4) a = 8 −14 R

Q16.Two identical parallel plate capacitors, of capacitance C each, have plates of area A, separated by a distance d . The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants K1, K2 and K3 . The first capaciitor is filled as shown in figure I, and the second one is filled as shown in figure II . If these two modified capacitors are charged by the same potential V , the ratio of the energy stored in the two, would be ( E1 refers to capacitor I and E2 to capacitor ( II ) ): E1 9K1K2K3 ( K1K2K3 ) ( K2K3 + K3K1K1 + K1K2 ) (1) (2) E1 = = E2 ( K1K2K3 ) ( K2K3 + K3K1K1 + K1K2 ) E2 K1K2K3 K1K2K3 ( K1K2K3 ) ( K2K3 (3) E1 + K3K1K1 + K1K2 ) (4) E1 = = E2 ( K1K2K3 ) ( K2K3 + K3K1K1 + K1K2 ) E2 9K1K2K3

Q16.The electric field in a region is given by →E = Ax + B ^i , where E is in NC-1 and 𝑥 is in metres. The values of constants are A = 20 SI unit and B = 10 SI unit. If the potential at 𝑥= 1 is V1 and that at 𝑥= - 5 is V2, then V1 - V2 is (1) 320 V (2) -520 V (3) 180 V (4) -48 V

Q16.A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants K1, K2, K3, K4 arranged as shown in the figure. The effective dielectric constant K will be: (1) K = ( K1+K2K1K2 + K3+K4K3.K4 ) (2) K = 2(K1+K2+K3+K4)(K1+K2)(K3+K4) (3) K = (K1+K4)(K2+K3) (4) K = (K1+K2)(K3+K4) 2(K1+K2+K3+K4) K1+K2+K3+K4

Q16.The galvanometer deflection, when key K1 is closed but K2 is open, equals θ0 (see figure). On closing K2 also and adjusting R2 to 5Ω, the deflection in galvanometer becomes θ05 . The resistance of the galvanometer is, then, given by [Neglect the internal resistance of battery]: (1) 12 Ω (2) 22 Ω (3) 5 Ω (4) 25 Ω

Q16.In the given circuit, an ideal voltmeter connected across the 10 Ω resistance reads 2 V . The internal resistance r , of each cell is: (1) 0 Ω (2) 1.5 Ω (3) 0.5 Ω (4) 1 Ω

Q16.Charges −q and +q , located at A and B, respectively, constitute an electric dipole. Distance AB = 2a, O is the mid point of the dipole and OP is perpendicular to AB. A charge Q is placed at P where OP = y and y ≫2a. The charge Q experiences an electrostatic force F . If Q is now moved along the equatorial line to P′ such that OP′= ( 3y ) the force on Q will be close to ( 3y ≪2a) (1) 27F . (2) F3 . (3) 3F . (4) 9F . JEE Main 2019 (10 Jan Shift 2) JEE Main Previous Year Paper

Q16.Voltage rating of a parallel plate capacitor is 500 V . Its dielectric can withstand a maximum electric field of 106V / m . The plate area is 10-4 m2 . What is the dielectric constant if the capacitance is 15 pF ? given ϵ0 = 8.86 × 10-12C2 / Nm2 (1) 3.8 (2) 8.5 (3) 4.5 (4) 6.2

Q16.A parallel plate capacitor is of area 6 cm2 and a separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constant K1 = 10, K2 = 12 and K3 = 14. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be: (1) 4 (2) 36 (3) 14 (4) 12

Q16.In the figure shown below, the charge on the left plate of the 10F capacitor is -30C. The charge on the right plate of the 6F capacitor is: (1) −12μC (2) +12μC (3) −18μC (4) +18μC

Q16.The parallel combination of two air filled parallel plate capacitors of capacitance C and nC is connected to a battery of voltage, V . When the capacitors are fully charged, the battery is removed and after that a dielectric material of dielectric constant K is placed the two plates of the first capacitor. The new potential difference of the combined system is: (1) (n+1)V (2) nV (K+n) K+n (3) V (4) V K+n

Q16.Seven capacitors, each of capacitance 2μF, are to be connected in a configuration to obtain an effective capacitance of ( 136 )μF. Which of the combinations, shown in figures below, will achieve the desired value? (1) (2) (3) (4)

Q16.A source of sound S is moving with a velocity of 50 m s-1 towards a stationary observer. The observer measures the frequency of the source as 1000 Hz . What will be the apparent frequency of the source when it is moving away from the observer after crossing him? (Take velocity of sound in air is 350 m s-1 ) (1) 750 Hz (2) 857 Hz (3) 1143 Hz (4) 807 Hz

Q17.A galvanometer, whose resistance is 50 ohm, has 25 divisions in it. When a current of 4 × 10−4 A passes through it, its needle (pointer) deflects by one division. To use this galvanometer as a voltmeter of range 2.5 V it should be connected to a resistance of: (1) 6250 ohm (2) 250 ohm (3) 6200 ohm (4) 200 ohm

Q17.Two equal resistances when connected in series to a battery, consume electric power of 60 W. If these resistance are now connected in parallel combination to the same battery, the electric power consumed will be : (1) 60 W (2) 240 W (3) 120 W (4) 30 W